Reducing global acquisition time is of main interest in medical magnetic resonance imaging (MRI), and even more when dynamic imaging such as fMRI is concerned. Actually, a short acquisition time allows improving the spatial/temporal resolution of acquired fMRI data, which leads to a more efficient statistical analysis. In addition, by reducing the global imaging time, some additional artifacts caused by the patient motion can be avoided. For this reason, parallel imaging systems have been developed: multiple receiver surface coils with complementary sensitivity profiles located around the underlying object or body are employed to simultaneously collect in the frequency domain (i.e. the so-called k-space), data sampled at a rate R times lower than the Nyquist sampling rate along at least one spatial direction, i.e. the phase encoding one; R is usually called the “reduction factor”. Therefore, the total acquisition time is R times shorter than with conventional non parallel imaging. A reconstruction step is then performed to build a full Field of View (FOV) image by unfolding the undersampled “elementary” images acquired by the individual receivers. This reconstruction is a challenging task because of the low Signal to Noise Ratio (SNR) in parallel MRI (pMRI) caused by aliasing artifacts related to the undersampling rate, those caused by noise during the acquisition process and also the presence of errors in the estimation of coil sensitivity maps.
The Simultaneous Acquisition of Spatial Harmonics (SMASH) [Sodickson et al., 1997] was the first reconstruction method, operating in the k-space domain. It uses a linear combination of pre-estimated coil sensitivity maps to generate the missing phase encoding steps.
Some other k-space based reconstruction techniques have also been proposed like GRAPPA (Generalized Autocalibrating Partially Parallel Acquisitions) [Griswold et al., 2002], and SENSE (Sensitivity Encoding) [Pruessmann et al., 1999]. SENSE is a two-step procedure relying first on a reconstruction of reduced FOV images and second on a spatial unfolding technique, which amounts to a weighted least squares estimation. This technique requires a precise estimation of coil sensitivity maps using a reference scan (usually a 2D Gradient-Echo (GRE)). It is presently the most frequently employed pMRI technique, applied in particular to brain and cardiac imaging.
For a general overview of reconstruction methods in pMRI see [Hoge et al., 2005].
SENSE is often supposed to achieve an exact reconstruction in the case of noiseless data and perfect coil sensitivity maps knowledge, which is also true for all above mentioned methods. However, in practice, the presence of noise in the data and inaccuracies in the estimation of coil sensitivity maps are unavoidable and make the reconstruction problem ill-conditioned.
As image reconstruction is an ill-posed inverse problem, regularization techniques are commonly applied to better estimate the full FOV image. Most of these techniques operate in the image domain; in particular, this is the case for Tikhonov regularization [Ying et al., 2004], which uses a quadratic penalty term either to promote smoothness constraints or to account for the squared difference between the reconstructed image and an a priori reference image. Despite the use of regularization, however, high reduction factors (exceeding a value of R=2) are generally considered unfeasible when low magnetic field intensities (up to 1.5 Tesla) are used, since the reconstructed images are affected by severe aliasing artifacts.
In [Chaâri et al. 2008] and [Chaâri et al. 2009] the present inventors have described a method of performing regularized image reconstruction in parallel MRI, using a wavelet-based regularization scheme, allowing to increase the reduction factor R.
The present invention aims at providing several improvements of said method, including extending it to dynamical imaging (e.g. fMRI) and making it fully or partially auto-calibrated (or “unsupervised”).